Khan Academy If you want clear explanations to most grade 7 & 8 concepts, you HAVE to go to the Khan Academy. Simply watching some of these video clip explanation should help improve your approach to explanation.
The Commutative Law of Multiplication (Steve R)
The Commutative Law of Multiplication is something that we take for granted, but when we really know what it means, then it is quite astonishing. I think that it is useful for teachers to have a deeper understanding of the fundamental properties of arithmetic, so here is an article that I wrote about the commutative law of multiplication. I had to embed the pdf because I can't seem to insert pictures into Wikispaces.
See my personal math Wiki if you're interested in a proof.
The Difference Between "Division" and "Quotient" (Steve R)
Back in school, you were probably told that "find the quotient" means the same as "divide". Well, it turns out that that is not quite true. Here is a video I made explaining the difference. http://screencast.com/t/Y2ExMTEx
Completing the Square (Steve H) I'm terrible at this and I know a lot of people still can't do this without looking up the "formula" to do it. However, there's a fundamental reason as to why you do the steps. I didn't "get it" until I saw it graphically (i.e. with shapes). Even in the khan academy videos, you don't really get to see it as pictures. Wikipedia, however, has a section that actually shows you how it's done geometrically: http://en.wikipedia.org/wiki/Completing_the_square#Geometric_perspective In case Wikipedia changes (which it often does), here is the image that should explain how to complete the square.
If you want clear explanations to most grade 7 & 8 concepts, you HAVE to go to the Khan Academy.
Simply watching some of these video clip explanation should help improve your approach to explanation.
The Commutative Law of Multiplication (Steve R)
The Commutative Law of Multiplication is something that we take for granted, but when we really know what it means, then it is quite astonishing. I think that it is useful for teachers to have a deeper understanding of the fundamental properties of arithmetic, so here is an article that I wrote about the commutative law of multiplication. I had to embed the pdf because I can't seem to insert pictures into Wikispaces.
See my personal math Wiki if you're interested in a proof.
The Difference Between "Division" and "Quotient" (Steve R)
Back in school, you were probably told that "find the quotient" means the same as "divide". Well, it turns out that that is not quite true. Here is a video I made explaining the difference.
http://screencast.com/t/Y2ExMTEx
Completing the Square (Steve H)
I'm terrible at this and I know a lot of people still can't do this without looking up the "formula" to do it. However, there's a fundamental reason as to why you do the steps. I didn't "get it" until I saw it graphically (i.e. with shapes). Even in the khan academy videos, you don't really get to see it as pictures. Wikipedia, however, has a section that actually shows you how it's done geometrically: http://en.wikipedia.org/wiki/Completing_the_square#Geometric_perspective
In case Wikipedia changes (which it often does), here is the image that should explain how to complete the square.
Geometer's Sketchapd
I found a pretty large list of links to Geometer's Sketchpad resources, so I thought I'd share.
http://mathfest.wikispaces.com/Resources+for+The+Geometer%27s+Sketchpad